The comparability graph of a tree \(t\)  is the simple graph with the same
vertices as \(t\) , but has an edge between two vertices whenever one is a
descendent of the other in \(t\) . A graph \((A,I)\)  is a transitive forest
if it is a disjoint union of comparability graphs of trees.
Wolk characterized transitive forests as those graphs that neither contain
\(\mathsf {P4}\)  nor \(\mathsf {C4}\)  (see Figure REF ) as an induced subgraph [1]}.
The main result of this section is:
